The Gospel for Easter 4 is the heart of our Lord's farewell discourse, and at it's center is the analogy of the woman in the pangs of child birth. This puts the picture of giving birth at the center of our Lord's teaching on the Holy Spirit. But really is it any surprise?
In John 1:12-13, those who receive the light, those who see and are enlightened, are given the right to become children of God, born "not of blood nor of the will of the flesh nor of the will of man, but of God."
In John 1:32-34, the He who has the Holy Spirit remaining with Him is He who is the Son of God. The Holy Spirit is associated with being a son of God. As John the Baptist proclaims: "I saw the Spirit descend from heaven like a dove, and it remained on him. I myself did not know him, but he who sent me to baptize with water said to me, ‘He on whom you see the Spirit descend and remain, this is he who baptizes with the Holy Spirit.’ And I have seen and have borne witness that this is the Son of God.”
In John 3, our Lord says that only those who are born again/from above, born of water and the Spirit, will see the kingdom of God. And this leads into a discussion with the Samaritan woman about the true children of God will worship God in Spirit and Truth. If you take the word and epexegetically, you get something like unto John 14 and 16, where the Spirit is the Spirit of Truth, the Spirit that is Truth, who will be made available and give life through the Word of God, through the Words of Jesus (John 6:53). And that Spirit of Truth will teach the sons of God and cause them to remember all the Jesus has spoken to them, his Words (John 14:26). Thus, the Spirit who remained with Jesus while He was with the Disciples (John 1:32-34), now makes Jesus to remain with the Disciples while He is with the Father (John 19:25-27; John 20).
In John 8, the Jews question Jesus about His Father, his genealogy. Our Lord flips this on the Jews and questions whether they are in fact the offspring of Abraham. For if they were truly the offspring of Abraham, they would do what Abraham did, which is rejoice to see Jesus' day. Abraham rejoiced and saw that day when the Father gave the word of promise to provide THE lamb for the burnt offering. Abraham kept the Word, which is Spirit and life (John 6:53). Thus whoever keeps Jesus' Word will never see death (8:50).
In John 9, the man born blind truly sees the Son of Man when he washes in the pool of Siloam.
In John 19, just before our Lord hands down the Spirit, he makes the beloved disciple the son of Mary the mother of Jesus (John 19:25-27).
All of this is to fulfill the Scriptures. For after the fall into sin, even though the woman's pain in childbearing would increase, God would give the seed born of the woman to crush the head of the serpent (the word for pain in Genesis 3 of the LXX is the same as John 16). Then in Genesis 4, Eve gives birth to Cain and says "I have gotten a man (ἄνθρωπον διὰ τοῦ θεοῦ, LXX) through the Lord." And as the hour of our Lord's glorification comes, the Roman governor proclaims "Behold, the man" (ἰδοὺ ὁ ἄνθρωπος; John 19:5). In other words: Look, see, this is the man promised to Eve.
The Holy Spirit then is pictured, in John at least, as the one who gives birth to Christians. The Holy Spirit is pictured as our mother.
And so, I think this changes the way we should understand John 16:5-15, especially the words παράκλητος and ἐλέγχω. I don't think they carry the judicial overtones of advocate and conviction, but rather more personal, so that what the Paraclete will do for the disciples and all Christians is what a mother does for her children. Mothers do more for her children than anyone else. Whatever the need, she can always be called upon to answer the need. For that is what the paraclete means: answering calls and needs when called upon. In giving birth, mothers feed, console, comfort, exhort, help, plead, and defend whenever called upon to do so. This is the picture John gives us of the Holy Spirit. It is also a picture that Paul gives:
"For our appeal (παράκλησις) does not spring from error or impurity or any attempt to deceive, but just as we have been approved by God to be entrusted with the gospel, so we speak, not to please man, but to please God who tests our hearts. For we never came with words of flattery, as you know, nor with a pretext for greed—God is witness. Nor did we seek glory from people, whether from you or from others, though we could have made demands as apostles of Christ. But we were gentle among you, like a nursing mother taking care of her own children. So, being affectionately desirous of you, we were ready to share with you not only the gospel of God but also our own selves, because you had become very dear to us.
"For you remember, brothers, our labor and toil: we worked night and day, that we might not be a burden to any of you, while we proclaimed to you the gospel of God. You are witnesses, and God also, how holy and righteous and blameless was our conduct toward you believers. For you know how, like a father with his children, we exhorted (παρακαλοῦντες) each one of you and encouraged you and charged you to walk in a manner worthy of God, who calls you into his own kingdom and glory." (1 Thess 2:3-13)
The word παράκλητος in John doesn't carry a judicial connotation, Neither, therefore, does the word ἐλέγχω. It should be understood in the same what it is used in Matthew 18:15 and Leviticus 19:17, which has the aim of showing fault with a view toward understanding, enlightenment, reconciliation. It is the act of a friend, of a brother, not a judge. It is what a mother does for her children. She studies her children to find out how she may effectively correct their faults and improve their character. She doesn't try to convict her children. She tries to make her children see so that they'll convict themselves, so that she can guide them nurture them into all the truth.
The nurture of the Spirit is not a grievance it has against the world, but a gift it is giving to the world. He enlightens, He shows the world with regard to sin inasmuch as unbelief in Jesus is the root of all sin. That is to say, the Spirit, the Paraclete is called upon to help and comfort and encourage when our conscience cries out "Lord, I believe, help my unbelief." With regard to righteousness, inasmuch as we no longer see Jesus because He went to the Father. That is to say, the Spirit, the Paraclete is called upon to help, comfort, and encourage by showing us the righteousness of Christ, which is declared to be ours because of His death, resurrection, and ascension. For where the Spirit is there is the Son of God, where the Spirit is there is the Word of God (John 6:53). With regard to judgment, inasmuch as the prince of this world has been judged. That is to say, the Spirit, the Paraclete is called upon to help, comfort, encourage by giving us freedom from the accuser to love our neighbor because God has first loved us. The Paraclete is called upon to help, encourage, and comfort by taking what belongs to our Lord and declaring it to us, making it ours. As a mother does for her children.
And all of this gives birth in us the life of the Spirit, the life of faith, the life of prayer. For we are no longer born children from this world, but born from the Father, through the Son, in the Holy Spirit. Ask, therefore, call upon the one who helps in times of need. And you will receive, that your joy may be full.